List colorings with measurable sets
نویسندگان
چکیده
منابع مشابه
List colorings with measurable sets
The measurable list chromatic number of a graph G is the smallest number ξ such that if each vertex v of G is assigned a set L(v) of measure ξ in a fixed atomless measure space, then there exist sets c(v) ⊆ L(v) such that each c(v) has measure one and c(v) ∩ c(v′) = ∅ for every pair of adjacent vertices v and v′. We provide a simpler proof of a measurable generalization of Hall’s theorem due to...
متن کاملExtracting List Colorings from Large Independent Sets
We take an application of the Kernel Lemma by Kostochka and Yancey [10] to its logical conclusion. The consequence is a sort of magical way to draw conclusions about list coloring (and online list coloring) just from the existence of an independent set incident to many edges. We use this to prove an Ore-degree version of Brooks’ Theorem for online list-coloring. The Ore-degree of an edge xy in ...
متن کاملBrooks’s Theorem for Measurable Colorings
Throughout, by a graph we mean a simple undirected graph, where the degree of a vertex is its number of neighbors, and a d-coloring is a function assigning each vertex one of d colors so that adjacent vertices are mapped to different colors. This paper examines measurable analogues of Brooks’s Theorem. While a straightforward compactness argument extends Brooks’s Theorem to infinite graphs, suc...
متن کاملNear-optimal list colorings
We show that a simple variant of a naive colouring procedure can be used to list colour the edges of a k-uniform linear hypergraph of maximum degree provided every vertex has a list of at least +c(log) 4 1? 1 k available colours (where c is a constant which depends on k). We can extend this to colour hypergraphs of maximum codegree o(() with + o(() colours. This improves earlier results of Kahn...
متن کاملMeasurable sets with excluded distances
For a set of distances D = {d1, . . . , dk} a set A is called D-avoiding if no pair of points of A is at distance di for some i. We show that the density of A is exponentially small in k provided the ratios d1/d2, d2/d3, . . . , dk−1/dk are all small enough. This resolves a question of Székely, and generalizes a theorem of Furstenberg-Katznelson-Weiss, Falconer-Marstrand, and Bourgain. Several ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Graph Theory
سال: 2008
ISSN: 0364-9024,1097-0118
DOI: 10.1002/jgt.20335